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Smoothed L-estimation of regression function

  • Ci­zek, P.
  • Tamine, J.
  • Härdle, W.

The Nadaraya-Watson nonparametric estimator of regression is known to be highly sensitive to the presence of outliers in data. This sensitivity can be reduced, for example, by using local L-estimates of regression. Whereas the local L-estimation is traditionally done using an empirical conditional distribution function, we propose to use instead a smoothed conditional distribution function. The asymptotic distribution of the proposed estimator is derived under mild [beta]-mixing conditions, and additionally, we show that the smoothed L-estimation approach provides computational as well as statistical finite-sample improvements. Finally, the proposed method is applied to the modelling of implied volatility.

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Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 52 (2008)
Issue (Month): 12 (August)
Pages: 5154-5162

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Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5154-5162
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  1. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
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  4. Fengler, Matthias R. & Härdle, Wolfgang K. & Villa, Christophe, 2001. "The dynamics of implied volatilities: A common principal components approach," SFB 373 Discussion Papers 2001,38, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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  6. Shinichi Sakata & Halbert White, 1998. "High Breakdown Point Conditional Dispersion Estimation with Application to S&P 500 Daily Returns Volatility," Econometrica, Econometric Society, vol. 66(3), pages 529-568, May.
  7. Pavel Cizek & Wolfgang Härdle, 2005. "Robust estimation of dimension reduction space," SFB 649 Discussion Papers SFB649DP2005-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, July.
  9. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521586115.
  10. Michal Benko & Wolfgang Härdle, 2005. "Common Functional Implied Volatility Analysis," SFB 649 Discussion Papers SFB649DP2005-012, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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